The flatness of a rolled product, e.g. a strip, is determined by the roll gap profile between the work rolls of a rolling mill and the thickness profile of the rolled strip. The strip flatness may then be influenced by manipulation of different control devices that affects the mill and its work roll gap profile. Such actuators may be mechanical devices such as work roll bending devices, intermediate roll bending devices, skewing or tilting devices, intermediate roll shifting devices, top crown actuators, or thermal devices such as work roll cooling/warming actuators etc.
In flatness control for cold rolling of metals, a number of actuators are used that influence the flatness profile. In the standard solution, the flatness deviations are mapped to the space of actuators with the help of a mill matrix, which describes the static flatness response from the respective actuators. This decomposition leaves a number of control loops, one for each actuator. These loops are equipped with PI controllers. Today, tuning of these controllers are based on off-line identification of models for each loop. In addition, known variations in the model, due to varying rolling speed for example, are taken into account in a parameter scheduling fashion. Two factors that make the process gain for each loop uncertain are its dependence on the rolled material, and possible discrepancy between the assumed mill matrix and the real behavior of the mill.
When rolling a strip, it is important to maintain the desired flatness profile at all times. Deviation from the desired flatness may result in costly strip breaks and scrap of produced coils. The task of the flatness control system is thus to drive the actual flatness profile as close as possible to the desired flatness profile, which put high requirements on the control system, in terms of calculation speed and accuracy.
Controllers for industrial processes need to be well tuned in order to reduce quality variations and keep the produced quality within specifications, in spite of varying conditions. In particular, a desire for a high production rate will often challenge the ability to control the process well enough to avoid both the production of off-spec material and interruptions in the production due to breakage. Sheet breakages in a paper machine or band rupture in a steel rolling mill are examples that may cause costly production losses.
The tuning of a controller is often based on a procedure to find a simple model from experiment data (from e.g. a step test) combined with a method to automatically find a good controller tuning, assuming this model to represent the behavior of the process well enough. For this procedure to be successful, it is essential that the model formulation is able to capture the actual behavior of the process during the experiment, and that the obtained model remains valid during the normal operation of the process with the varying conditions that may occur. The tuning method may allow some variation around the assumed nominal behavior, by putting a suitable degree of focus on robustness. If there are essential variations in process dynamics—for example with varying production speed—known such variations should be handled via parameter scheduling. If the variations occur during the tuning experiment, the model identification will be seriously disturbed if standard methods are applied.
A common approach is black-box identification that is to estimate the parameters in a discrete time formulation of the model, expressed for the same sampling period as used in the actual control. However, in the cases where some process dynamics vary with the production speed, the estimation will be disturbed by speed variations, since the true parameter values of the model will vary. This holds both if sampling is made per time unit, which is the most common case, since then the parts of the dynamics that do vary with speed will give varying discrete time model parameters, and if sampling is done per amount of material flow, which sometimes is done for practical reasons and also gives constant discrete time model parameter values for dynamics which have time characteristics proportional to the inverse of the speed, since then the parts of the dynamics that do not vary with production speed will give varying discrete time model parameters.
For the tuning of the PI control loops, in the standard solution for flatness control, varying rolling speed prevents use of black-box identification methods to determine a model. Sampling is performed per length unit. So the model of transport behavior would be invariant for sampled data, but the actuator dynamics does not get an invariant model for data sampled this way, and therefore the whole discrete time model will vary. In addition, the sampling period may vary due to a varying down-sampling multiple, and varying pre-filtering in relation to this, as well.
To obtain accurate control, the controllers should be well tuned, based on how the process responds to changes of manipulated variables. The gain of the rolling process depends on a number of parameters that are not well known. For flatness control, the relevant gains are influenced by what material is being rolled, the actual agreement of the assumed mill matrix with reality, and other things.
After separation of the original control task, i.e. maintained flatness across the width of the produced material using several actuators, into several actuator-measurement loops, the current control strategy is based on standard control loop tuning during commissioning. Normally this is done as a single estimation of model parameters off-line for each loop and tuning for that model. To make this activity more efficient, the relevant model parameters should be estimated on-line and presented to the user in real time for decision when to end the activity. Further, the estimation should be performed in a way that is not disturbed by speed variations.
One problem is that if the process or the material changes, the control may become inaccurate, even if it has been accurate previously, which leads to poor product quality or to scrap. The change in material may, for example, cause changes in properties such as thickness, width, or hardness of the material. After a change of material, the control has to be adapted to the properties of the new material. The faster the control is adapted to the new properties, the faster the quality of the production is restored.
To avoid that problem adaptive control could be applied. Adaptive control usually applies black-box models. However, discrete time models with varying sampling period due to varying speed will have varying parameter values, due to the time invariant actuator associated dynamics. Thus adaptive control based on black-box identification of such models will be useless.
A problem in connection with tuning controllers for industrial processes with varying material flow rate, such as flatness measurement during rolling, is that the sampling rate of the measuring of the controlled property is dependent on the flow rate, such as the rolling speed, which leads to varying sampling intervals. It is easy and known to estimate a parameter for a time discrete model. However, it is not possible to use a time discrete model for tuning controllers for processes with varying material flow rate due to the variable sampling intervals.